What is the graph of the inequality? 4x + 2y is less than or equl to 6

Weren't there some answer choices from which to choose?

You can answer this question without those choices, however.  Solve the given inequality 4x + 2y ≤ 6 for y:

x + (2/4)y ≤ 6/4, or

x + (1/2)y ≤ 3/2             subtract x from both sides

-x                 -x

(1/2)y ≤ -x + 3/2,

or    y ≤ -2x + 3

Graph the str line y = -2x + 3, using a solid like (due to the "less than or 
                                                equal to" symbol)

This line has y-intercept (0,3) and slope m = -2.  Plot (0,3) and thru it draw a straight line with slope m = -2 (it will slope downward as you move to the right).

Now shade (darken) the region BELOW this line  (due to the "less than or 
                                                equal to" symbol)